1. Hints. The one with the most molecules has the most moles. (Remember Avogadro's number?) What equation do you know that relates these four quantities: moles, volume, pressure, and temperature?
 
 

2. Hints. Review Avogadro's Law, pp. 549-550 in Kotz and Treichel.
 
 

3. Worked Example. Complete combustion of a 0.0125 mol sample of a hydrocarbon, C_xH_y, gives 0.840 L of carbon dioxide at STP and 0.675 g water.

(a) What is the molecular formula of the hydrocarbon?
(b) What is the empirical formula of the hydrocarbon?

Every mole that burns gives you 4 moles of CO₂ (same number of moles as the number of carbons in butane) and 5 moles of H₂O (half the number of moles as the number of hydrogens; the 10 hydrogens in butane can only give 5 moles of water since each water molecule contains two hydrogen atoms). This is true for all hydrocarbons: thus

Solution. First get the moles of carbon dioxide and water from what we are given.

0.840 L CO₂ at STP x (1 mol CO₂ / 22.4 L at STP) = 0.0375 mol CO₂

0.675 g H₂O x (1 mol H₂O/18.02 g H₂O) = 0.0375 mol H₂O

So, 0.0125 mol of C_xH_y gave 0.0375 mol CO₂ and 0.0375 mol H₂O. This means that x = (0.0375/0.0125) = 3 and y/2 = (0.0375/0.0125) = 3, or y = 6.

(a) Thus the molecular formula is C₃H₆.

(b) The empirical formula is CH₂.

5. Hints and Worked Example. A 3.00-L bulb containing He at 145 torr is connected by a valve to a 2.00-L bulb containing Ar at 355 torr. (See the figure for Question 82, p.579 in Kotz and Treichel 4th edition for the experimental setup.) The valve between the two bulbs is opened and the two gases mix.

(a) What is the partial pressure (torr) of He?
(b) What is the partial pressure (torr) of Ar?
(c) What is the total pressure?
(d) What is the mole fraction of He?

Solution. When the valve is opened between the two bulbs, the gases will mix rapidly and reach equilibrium. Each gas will now have a total volume of 5.00 L to occupy (2.00 L + 3.00 L).

The partial pressures of each gas can be obtained from Boyle's law (PV = constant = P'V'), where P and V are the original pressure and volume (before the valve is opened), V' is the volume after the valve is opened, and P' is the new pressure (the partial pressure in the mixture).

The total pressure is the sum of the partial pressures of each gas.

The mole fraction of He is the pressure of He divided by the total pressure.

Thus the partial pressure of helium after mixing is

(145 torr He before mixing)(3.00 L) = (P_He after mixing)(5.00 L)
P_He after mixing = 87.0 torr

Similarly, the partial pressure of argon after mixing is 142 torr.

The total pressure after mixing is 87.0 torr + 142 torr = 229 torr.

The mole fraction of helium is P_He/P_tot = 87.0 torr/229 torr = 0.380
 
 

Use the Maxwell equation (equation 12.14) to find the rms speed of the slowest-moving molecule.
 
 

7. Hints. See Example 12.12 in Kotz and Treichel. Once you have found the pressure due to oxygen alone, use the ideal gas equation to find the number of moles of oxygen. Then from the balanced equation you can determine the moles of potassium chlorate and from this, the mass of potassium chlorate in the sample. You can now calculate the % KClO₄.
 
 

8. Hints. See Exercise 12.15 in Kotz and Treichel, p. 573. Answer is in the back of the book.

This page is http://chemiris.labs.brocku.ca/~chemweb/courses/chem181/CHEM_1P81_Assign_3.html
Last revised: January 5 2001 by M. F. Richardson
© Brock University, 2001